On a class of $5$-manifolds with ${\pi }_1=\mathbb{Z}$ with applications to knottings in $S^5$

Matthias Kreck, Yang Su

We classify $5$-manifolds with fundamental group $\mathbb{Z}$ and ${\pi }_2$ a finitely generated abelian group in terms of the cup product on the second cohomology of the universal co…